Impact of changes in the Sun s conveyor belt on recent solar cycles

Transcription

1 Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 37,, doi: /2010gl044143, 2010 Impact of changes in the Sun s conveyor belt on recent solar cycles Mausumi Dikpati, 1 Peter A. Gilman, 1 Giuliana de Toma, 1 and Roger K. Ulrich 2 Received 28 May 2010; revised 17 June 2010; accepted 22 June 2010; published 30 July [1] Plasma flowing poleward at the solar surface and returning equatorward near the base of the convection zone, called the meridional circulation, constitutes the Sun s conveyor belt. Just as the Earth s great oceanic conveyor belt carries thermal signatures that determine El Nino events, the Sun s conveyor belt determines timing, amplitude and shape of a solar cycle in flux transport type dynamos. In cycle 23, the Sun s surface poleward meridional flow extended all the way to the pole, while in cycle 22 it switched to equatorward near 60. Simulations from a flux transport dynamo model including these observed differences in meridional circulation show that the transport of dynamo generated magnetic flux via the longer conveyor belt, with slower return flow in cycle 23 compared to that in cycle 22, may have caused the longer duration of cycle 23. Citation: Dikpati, M., P. A. Gilman, G. de Toma, and R. K. Ulrich (2010), Impact of changes in the Sun s conveyor belt on recent solar cycles, Geophys. Res. Lett., 37,, doi: /2010gl Introduction [2] Two observational techniques, in particular, Doppler shifts [Hathaway et al., 1996; Ulrich and Boyden, 2005] and helioseismic [Basu and Antia, 2010] techniques, have revealed a poleward meridional plasma flow with a speed of m s 1 in the upper part of the Sun s convection zone. Conserving mass, the flow sinks down at high latitudes and returns towards the equator near the base of the convection zone, closing the circulation loop. Solar meridional circulation is one of the most important ingredients in a class of solar dynamo models, called the flux transport dynamos [Wang and Sheeley, 1991], which are successful in reproducing many solar cycle features. This circulation acts as a conveyor belt that carries a remnant of the surface magnetic flux produced from the decay of active regions from the surface to the base of the convection zone, where this remnant flux gets amplified by the Sun s differential rotation to generate spotproducing magnetic fields. Solar meridional circulation plays an important role in determining the dynamo cycle period [Dikpati and Charbonneau, 1999] and in governing the memory of the Sun s past magnetic fields. [3] The Sun s meridional circulation is analogous to the latitudinal circulation in the great ocean conveyor belt, which is a thermohaline circulation driven primarily by the formation and sinking of cold water in the Norwegian Sea. This circulation is thought to be responsible for the large flow of 1 High Altitude Observatory, National Center for Atmospheric Research, Boulder, Colorado, USA. 2 Department of Physics and Astronomy, University of California, Los Angeles, California, USA. Copyright 2010 by the American Geophysical Union /10/2010GL upper ocean water from the tropical Pacific to the Indian Ocean through the Indonesian Archipelago. A high latitude cooling along with a low latitude heating drives a southward flow from north polar latitudes, and a net high latitude freshwater accumulation together with a low latitude evaporation creates a counterflow from the Pacific to the North Atlantic. Warm North Atlantic meridional overturning circulation is linked to excessive rain fall over Sahel and western India, while variations in overturning flow in the eastern Pacific determine the timing, amplitude and duration of an El Nino event [Knauss, 1996]. [4] There are many common features between the Sun s meridional flow conveyor belt and that of the ocean, namely both are persistent slow flow in the turbulent medium and both carry the surface forcing (surface magnetic flux and thermal patterns respectively in the case of the Sun and the ocean) with long memory. The variations in the meridional flow speed and its latitudinal distribution may largely determine the solar cycle timing and also contribute to both shape and strength. 2. Construction of Conveyor Belt [5] Ulrich and Boyden [2005] showed that the average meridional plasma flow in major part of cycle 23 was poleward all the way to the poles. Surface Doppler measurements made at Mount Wilson have been extended through 2009 and are shown in Figure 1a. Surface Doppler measurements are, so far, the only measurements that give us information about the latitudinal pattern of surface meridional plasma flow during cycles 22 and 21. These measurements show evidence of persistent reversed flow poleward of latitude 60 degrees during the major part of cycle 22 (see Figure 1a and also Figure 1f). Note that while the latitudinal resolution is degraded at high latitudes, a higher fraction of the plasma flow is measured in the line of sight, allowing such measurements all the way to the pole. Also note that plasma flow can only be reliably measured by surface Doppler or helioseismic methods, not by magnetic feature tracking. Featuretracking speeds should instead be compared to the output of dynamo and surface transport models. [6] Taking guidance from these surface observations of the Sun s latitudinal distribution of the meridional flow pattern, we construct the meridional circulation in the entire convection zone by invoking the constraint of mass conservation that includes an adiabatic density stratification in the solar convection zone. Models for the full dynamical system virtually all use the anelastic approximation, for which the departures from an adiabatic density stratification are insignificant for the mass flux and the mass continuity equation. Thus the streamlines constructed for the meridional flow in the way described above and in details in the supporting material capture the essential differences between cycle 22 1of6

2 Figure 1 2of6

3 conveyor belt with slower return flow in cycle 23 compared to that in 22 caused the unusually long duration of cycle 23. Figure 2. Percentage change in equatorward return flow speed at the base of the convection zone at latitudes 20 degree (blue), 15 degree (green), 10 degree (yellow) and 5 degree (red), as a function of the latitude extent of the primary flow cell. and 23. These streamlines are shown in Figures 1b and 1c respectively, and the velocity vectors for these two flows in Figures 1d and 1e. Note that the streamline represent the mass flux whereas the arrow vectors represent flow velocities. [7] The major differences are (i) the longer conveyor belt for cycle 23 due to the continuation of the poleward flow all the way to the poles, and (ii) a slower return flow at lowlatitudes (equatorward of 25 degree) in cycle 23 compared to cycle 22. While the longer conveyor belt in cycle 23 is immediately evident in both streamlines plots and vector plots, it is not easy to see the slower return flow at lowlatitudes in Figure 1e compared to Figure 1d. So we plot in Figure 2 the percentage change in the equatorward returnflow speed as a function of the latitude extent of the primary flow cell. [8] What is the sensitivity of the dynamo cycle period to the latitudinal extent of the dominant meridional flow cell? Can these variations in the Sun s conveyor belt from cycle to cycle tell us anything about the cycle features, such as cyclelengths, cycle amplitudes or shapes, particularly when cycle 23 has behaved so differently from cycle 22? In particular, can these differences in the conveyor belts in cycles 22 and 23 explain why cycle 23 lasted unusually long, about 12.5 years, while cycle 22 about 10.5 years? Can these differences give us any clue about the amplitude of cycle 24 that has just begun? We hypothesize that the longer 3. Theoretical Prescription of Dynamo Ingredients [9] Given the observational evidence for solar meridional flow changing the latitude of its peak, and at times having a weak second cell in high latitudes, we consider the stream function, y which is related to the spherical polar function Y as Y = yr sin, so that constant yr sin contours give the streamlines. We prescribe Y (= yr sin) in expression (1), which captures the solar like meridional circulation features in the simplest way. Many other choices are possible, but this is a very robust construction of meridional circulation cell. r sin ¼ 0 ð 0 Þsin ð r R bþ 1 e 1r ðr R b Þ 1 e 2rð =2Þ e ððr r0þ=gþ2 ð1þ Using the constraint of mass conservation, the velocity components (v r, v ) can be computed from rv = r Y ^e as follows: v r ¼ 1 r 2 sin v ¼ 1 r ð r sin ð r sin Þ: A density profile for an adiabatically stratified solar convection zone is r(r)=r b [(R/r) 1] m (r b denotes the density at the depth R b, near convection zone base) with m = 1.5. For all practical purposes, we use r(r)=r b [(R/r) 0.97] m, in order to avoid an unphysical infinite flow at the surface. [10] The parameters within equation (1) do the following: y 0 determines the maximum speed of the flow; 0 sets the colatitude where the primary poleward flow cell ends and the secondary equatorward cell begins it ranges from 0 to 45 degrees; R denotes the solar radius and R b the radius near the bottom of the convection zone down to which the flow penetrates; b 1 and b 2 control how concentrated the flow will be at the pole and equator, respectively;, taken slightly greater than 2, keeps the flow nonsingular at the pole; and r 0 and G are parameters that determine where the streamfunction maximum is and where the streamlines are concentrated. This kind of stream function has been used by many other fluxtransport dynamo modellers over the past 15 years. [11] The values we take for these parameters are: R b = 0.69R, b 1 = 0.1, b 2 = 0.3, = , r 0 =(R R b )/5, G = 3 and r b = 0.2 gm/cc. For these choices the poleward surface flow maximizes at 24 and the high flow speed Figure 1. (a) Meridional plane velocity measurements from Mount Wilson synoptic program. The value of colors on the map are given in the scale at right. The line of sight uncorrected flow has been averaged over all longitudes for 2 Carrington rotations. Top two brackets show the durations of cycles 22 and 23. The semi transparent strip around 55 degree N latitude shows that the primary poleward cell in cycle 22 mostly ended there and is replaced by a second cell with equatorward surface flow above that latitude, while in cycle 23 the primary cell continued all the way to the pole. (b and c) Two circulation patterns represented by streamlines in the pole to equator meridional cut. The contours of the spherical polar streamfunction have been plotted in logarithmic interval with 3 contours covering one order of magnitude. (d and e) The corresponding velocity vectors. (f) The average surface flow speeds in cycles 22 and 23, as function of latitude, after line of sight correction. 3of6

4 [14] The diffusivity profile used is a 3 step profile in depth, given by (4) (for more details, see Dikpati et al. [2006]). ðþ¼ r core þ T 2 1 þ erf r r 4 þ super r r 5 1 þ erf : d 4 2 d 5 ð4þ Figure 3. A two dimensional map of dynamo cycle period, obtained from the simulations of a flux transport dynamo, as function of latitude extent of primary meridional flow cell and maximum poleward surface flow speed. Thick continuous white line denotes the contour of an 11 year cycle period. Thin white lines denote the contours of other periods in halfyear intervals. The horizontal broken line marks the maximum surface flow speed of 14 meters/sec. The positions of cycles 22 and 23 in this map are shown by semi transparent gray patches. occurs in the latitude range To obtain a maximum poleward flow speed of 14 m s 1 at the surface, we use y 0 72, 112 respectively for a single cell all the way to the pole, and for a poleward cell equatorward of 65 degree latitude. By varying y 0 we vary the flow speed. [12] The differential rotation pattern used in this calculation is the same as used by Dikpati et al. [2004], given in their expression (3), with all parameters the same except d1 which is 0.025R instead of 0.05R, representing a slightly thinner tachocline. [13] The amplitude of the Babcock Leighton source, in units of velocity, is about 1.12 m s 1, while the bottom alphaeffect is a factor of 30 smaller. The amplitudes and profiles of these two sources of poloidal fields are similar to those used in many previous studies. We write down the mathematical forms for these two a effects in expressions (3a) and (3b). S BL ðr;þ ¼ s þ erf r r 1 r r 2 1 erf d 1 d 2 2 sin cos 1 þ e 1 ð 3 Þ ; ð3aþ S tachocline ðr;þ ¼ s þ erf r r 3 d 3 : sin 6 2 e 2 ð 4Þ 2 3 ½e ð =3 Þ þ 1Š 1 erf r r 4 d 4 ð3bþ The parameter values used in (3a) and (3b) are: s 1 = 2.5, s 2 = 0.05, r 1 = 0.95R, r 2 = 0.987R, r 3 = 0.706R4, r 4 = 0.725R, d 1 = d 2 = d 3 = d 4 = R, g 1 = 5.0, g 2 = 70.0, g 3 = The parameter values are: h super = cm 2 s 1 which works in a thin layer at the surface, h T cm 2 s 1 which works in the bulk of the convection zone and h core =10 9 cm 2 s 1, below the base of the convection zone down to 0.6R. The thickness of the three layers with different diffusivities and the transitions between adjacent layers are specified by r 4 = 0.725R, d 4 = R, r 5 = 0.956R, d 5 = 0.025R. [15] Including the above meridional flow with wide range of values for 0 and a wide range of values for the maximum poleward surface flow speeds, we have solved the fluxtransport dynamo equations in their commonly used form, such as described by Dikpatietal.[2004] [see also Dikpati and Gilman, 2007]. 4. Results [16] In order to test our hypothesis we performed the simulation runs of a flux transport dynamo model with a wide range of latitudinal extent of the primary flow cell and of peak meridional flow speed. We vary the latitudinal extent of the primary cell from 60 to 90 degrees and the peak flow from 10 to 20 m s 1. The results are shown in Figure 3 in the form of a two dimensional map. [17] For a fixed poleward surface flow speed, we see a systematic increase in dynamo cycle period with the increase in the latitude extent of the primary cell. The increase in cycle period is about 20% for high meridional flow with speed 18 m s 1 and higher, whereas it is 30% for flow speeds of 12 m s 1 or lower. For a fixed size of the primary cell, the dynamo cycle period decreases with increasing flow speed, a result already noted before [Wang and Sheeley, 1991; Dikpati and Charbonneau, 1999]. Observations indicate that the maximum poleward surface flow speeds during the major parts of cycles 22 and 23 are both about m s 1. The difference in the latitude extent of the primary meridional flow cell creates the differences in the path lengths of the conveyorbelts as well as the differences in the equatorward return flowspeed at and near the base of the convection zone in an extended latitude zone equatorward of 25 degree. It is, therefore plausible that these differences may have caused the difference in observed periods of cycles 22 and 23. The reduction in flow speed in low latitudes is particularly important, because this is the region where the spot producing strong toroidal fields occur. [18] A timely issue is what the presence or absence of a high latitude reverse meridional flow cell does to the strength of the polar fields. To make a valid comparison of polar field amplitudes, the flow amplitudes of the primary flow cell and the poloidal field sources were kept the same in our simulations. We find that the maximum amplitude of the surface radial fields (B rmax 57 Gauss) occurs around 85 latitudes when the primary meridional flow cell extends all the way to the pole, whereas B rmax ( 54 Gauss) occurs around 65 latitudes when the primary flow cell ends at 70 with a reversed cell beyond that. This is expected because the flow is con- 4of6

5 verging to the boundary between the cells from both poleward and equatorward sides. This was extensively demonstrated by Jouve and Brun [2007] and also discussed by Dikpati et al. [2004]. Recently such a shift of peak polar field from the pole to the boundary between two cells was found by Jiang et al. [2009], using a surface transport model. But unlike in our case, their shifted peak also got significantly reduced in amplitude. The lack of reduction in amplitude of the shifted peak in our case could be due to our solving for the poloidal vector potential, A,(B p = r A ^e ), in the presence of strong convergence of the flow either at the poles or at the interface between the two cells, in both cases accompanied by a sinking flow towards the low magnetic diffusivity regions. [19] What happens to the polar field amplitudes in a measurement depends on how and at what latitudes the polar field is being measured. For example, at 85 latitudes at the surface, B r is about 3 times larger in the single cell case than in the case with the high latitude reverse cell. By contrast, at 65 latitudes B r in the case with the high latitude reverse cell is about 2 times larger than B r in the single cell case. Noting that the observed polar fields from Wilcox Solar Observatory is instrumentally averaged over the latitude range from 55 to the pole, the model output that should be compared with observations is actually a weighted integral (hb r i = R 2 R 2=5:143 B r R 2 sin dd 0 0 R 2 R 2=5:143 R 2 sin dd 0 0 ) which accounts for the variation in area with latitude. Performing this integration, we find that the integrals in the two cases are almost the same, namely 14 and 16 Gauss in the single cell and two cell cases respectively. This indicates that the presence or absence of a reverse cell only rearranges the radial magnetic fields in latitude. If we would have applied a procedure to compute polar fields in the way they are measured by NSO Kitt Peak (see Arge et al. [2002] for details), the average polar fields in a small latitude range around 75 would be substantially higher in the two cell case with the primary cell reversing around 70. In that case the differences in the meridional flow patterns seem to account for the weaker polar fields in cycle 23 compared to that in cycle 22, but the amplitude of polar field is determined by many factors the amplitude of the polar field source, time variation in meridional flow, tilt angles of bipolar active regions and turbulent magnetic diffusivity being the important ones. 5. Discussions [20] With our prior knowledge of flow observations [Basu and Antia, 2003], namely the slowdown of meridional flow during the rising phase of the solar cycle 23 ( ), a delayed onset of cycle 24 was predicted [Dikpati, 2004]. With further advancement in flow measurement techniques, we now know the latitudinal distribution of the Sun s meridional flow and therefore, can more accurately estimate how long a solar cycle will continue. [21] Our results are based on large cells extending down to the base of the convection zone, a choice supported by hydrodynamic models of differential rotation and meridional circulation [Rempel, 2005]. However, complex choices of many cells stacked in latitude and depth are also possible [Jouve and Brun, 2007]. These and other flux transport dynamo simulations show that the cycle period does not depend strongly on the precise form of the stream function, but instead on its most global properties, such as how many circulation cells in latitude and depth it has. [22] The changes observed recently in the conveyor belt may also explain why the minimum at the end of cycle 23 was so long compared to previous minima, namely the greater slow down in the return flow as the magnetic flux gets carried closer and closer to the equator made the minimum phase of cycle 23 last longer, allowing more time for the last spotproducing toroidal field to erupt or be cancelled out at the equator by the opposite hemisphere counterpart. This could have contributed to the deepness of the minimum between cycles 23 and 24. [23] The longer and slow moving conveyor belt at high latitudes, late in cycle 23, also gives the new toroidal fields of cycle 24 more time to be amplified by the differential rotation at the base of the convection zone before they reach sunspot latitudes. This hints that cycle 24 should be a stronger cycle than 23 [Dikpati et al., 2006]. However, note that the magnetic memory and the surface polar field sources play bigger roles in determining respectively the cycle strength and polar fields strength, whereas the meridional flow plays a bigger role in the determining the shape and the duration of a cycle. [24] We have demonstrated the importance of the latitude location of the switch from poleward flow to equatorward flow at the surface in determining the period of the solar cycle. There are hints from Mount Wilson meridional flow data that there was a high latitude equatorward flow cell at the surface during cycles 19 through 21 also. All these cycles had periods between 10 and 11 years, which is consistent with what the model would produce. It might be possible to even go back further in time, if the equatorward flow cell could be inferred from such features as polar faculae [Sheeley, 1991]. In principle, all past and future cycle durations could be plotted on the map of Figure 3 if meridional flow speed and the extent of its primary cell can be measured. [25] Our model calculation here is limited by our taking a steady meridional flow that represents an average over an entire cycle. In the future, it would be more realistic to include a time varying meridional flow in a dynamical flux transport dynamo model, but such a model has not yet been built. [26] There are alternative explanations of long cycles followed by low minima that depend on the Waldmeier effect [Cameron and Schüssler, 2007] as well as the model of Kitiashvili and Kosovichev [2008] which performs remarkably well in predicting solar cycles while also reproducing the Waldmeier effect, without relying on a meridional circulation. [27] Acknowledgments. We thank Paul Charbonneau for his critical reading of the paper and for his helpful comments. We extend our thanks to the two external reviewers for their helpful comments, taking care of which improved the paper significantly. This work is partially supported by NASA grant NNX08AQ34G. The National Center for Atmospheric Research is sponsored by the National Science Foundation. References Arge, C. N., E. Hildner, V. J. Pizzo, and J. W. Harvey (2002), Two solar cycles of nonincreasing magnetic flux, J. Geophys. Res., 107(A10), 1319, doi: /2001ja Basu, S., and H. M. Antia (2010), Characteristics of solar meridional flows during solar cycle 23, Astrophys. J., 717, 488, doi: / x/ 717/488. Cameron, R., and M. Schüssler (2007), Solar cycle prediction using precursors and flux transport models, Astrophys. J., 659, Dikpati, M. (2004), Global MHD theory of tachocline and the current status of large scale solar dynamo, in Proceedings of the SOHO 14/GONG 5of6

6 2004 Workshop Helio and Asteroseismology [Electronic Resource]: Towards a Golden Future : July 2004 New Haven, Connecticut, USA, edited by D. Danesy, Eur. Space Agency Spec. Publ., ESA SP 559, 233. Dikpati, M., and P. Charbonneau (1999), A Babcock Leighton flux transport dynamo with solar like differential rotation, Astrophys. J., 518, Dikpati, M., and P. A. Gilman (2007), Steps for building a calibrated fluxtransport dynamo for the Sun, Sol. Phys., 241, 1 5. Dikpati, M., G. de Toma, P. A. Gilman, c. N. Arge, and O. R. White (2004), Diagnostics of polar field reversal in solar cycle 23 using a flux transport dynamo model, Astrophys. J., 601, Dikpati, M., G. de Toma, and P. A. Gilman (2006), Predicting the strength of solar cycle 24 using a flux transport dynamo based tool, Geophys. Res. Lett., 33, L05102, doi: /2005gl Hathaway, D., P. Gilman, J. Harvey, F. Hill, R. Howard, H. Jones, J. Kasher, J. Leibacher, J. Pintar, and G. Simon (1996), GONG observations of solar surface flows, Science, 272, Jiang, J., R. Cameron, D. Schmitt, and M. Schüssler (2009), Countercell meridional flow and latitudinal distribution of the solar polar magnetic field, Astrophys. J., 693, L96 L99. Jouve, L., and A. S. Brun (2007), On the role of meridional flows in flux transport dynamo models, Astron. Astrophys., 474, Kitiashvili, I., and A. G. Kosovichev (2008), Application of data assimilation method for predicting solar cycles, Astrophys. J., 688, L49 L52. Knauss,J.A.(1996),Introduction to Physical Oceanography, Prentice Hall, Upper Saddle River, N. J. Rempel, M. (2005), Solar differential rotation and meridional flow: The role of a subadiabatic tachocline for the Taylor Proudman balance, Astrophys. J., 622, Sheeley, N. R., Jr. (1991), Polar faculae , Astrophys. J., 374, Ulrich, R. K., and J. E. Boyden (2005), The solar surface toroidal magnetic field, Astrophys. J., 620, L123 L127. Wang, Y. M., and N. R. Sheeley Jr. (1991), Magnetic flux transport and the Sun s dipole moment: New twists to the Babcock Leighton model, Astrophys. J., 375, G. de Toma, M. Dikpati, and P. A. Gilman, High Altitude Observatory, National Center for Atmospheric Research, 3080 Center Grn., Boulder, CO 80301, USA. (dikpati@ucar.edu) R. K. Ulrich, Department of Physics and Astronomy, University of California, Box , Knudsen Hall, Los Angeles, CA , USA. 6of6